BONDS AND INTERMOLECULAR FORCES
In the study of proteins, atoms that are not part of molecules
will rarely be encountered. Most atoms have interacted with other
atoms to form either covalent or ionic bonds. After these bonds
have formed it is still possible for further interactions to
occur through a series of secondary interactions. These secondary
forces are very important to the structure of proteins and will
be discussed in detail. First, however, the more familiar primary
bonds will be discussed to establish the nature and strength of
the forces involved in their formation.
Covalent Bonds
When two atoms share electrons to fill their valence shells, the resulting bonds are termed covalent. The sharing of electrons lowers the energy of the system partially through the magnetic attractions of electrons having opposite spins. The bond energy of covalent bonds is actually a measure of the free energy gained in going from the non-bonded to the bonded state. These are strong bonds with energies around 80 - 100 kcal/mole.
Once a covalent bond is formed it may be a polar or nonpolar one. In symmetrical molecules like carbon tetrachloride:
The electrons are evenly distributed around the nuclei involved and the molecules are electrically neutral. In structures like water:
The molecules are neither symmetrical nor are they completely
electrically neutral. The oxygen atom has a greater attraction
for electrons than does the single proton of the hydrogen atom. (
Oxygen is said to be more electronegative than hydrogen ). These
bonds have what is called a partial ionic character which tends
to strengthen them. It also means that the molecules that make up
such bonds may or may not have partial electrical charges.
In the example of carbon tetrachloride, the chlorine atoms attract the electrons more than does the carbon nucleus. Hence the molecule may be drawn:
with partial negative and positive charges. The symmetry of the charges results in a neutral molecule.
In the case of water, the asymmetry of the molecule yields to a situation where the charges do not balance:
and the molecule has definite positive and negative portions.
Such a molecule is called a dipole. The interaction of dipoles
with themselves, with other dipoles, with ions and with molecules
that can be induced to become dipoles are important to the
structure of proteins and will be discussed in detail later. The
vast majority of the primary bonds in proteins will be strong
covalent ones. Some of these will have a dipole nature while
others will lack it. Both types of bonds make important
contributions to the ultimate structure of protein molecules.
Ionic Bonds
Covalent bonds can have from 0% ionic nature for nonpolar molecules to some higher percentage for polar compounds. For example, H-O bounds are about 40% ionic in nature. The case where the bond becomes 100% ionic is when electrons are not shared, but are actually transferred from one atom to another. Such a transfer of electrons results in the formation of an ionic bond. When an atom of sodium transfers an electron to an atom of chlorine the result is the creation of two ions:
Na+
and
When other Na+ and Cl- ions are present, the Na+ ion tends to be surrounded by Cl- ions and the Cl- ions are surrounded by Na+ ions. There is no real molecule of NaCl as such, but rather an extensive array of interacting ions.
The energy of ionic bonds can be related by Coulomb's law to the work required to bring two charges separated by an infinite distance to some finite distance of separation, r. For two molecules, A and B:
Where q1 = ZAe which is equal to the product of the number of charges on A and the charge of one electron, e. Similarly, q2 =ZBe and r is the distance between the centers of charge and D is the dielectric constant.
The dielectric constant is the ratio of the force between two
charges in a vacuum compared to the force of the two charges in
some other medium. By definition the dielectric constant of a
vacuum is one and by measurement it is found to be about 80 for
water. Instead of work the relation of the charges may be
expressed as the potential energy of the system:
In the case of Na+Cl-, and given the distance of separation of the Na+ and Cl- ions ion a crystal and the charge of an electron and assuming that D ª 1 in the crystal, a value for the bond energy of 120 kcal/mole is obtained. This suggests that to break the Na+Cl- bond 120 kcal/mole of energy must be applied. It would thus appear that considerable energy would have to be applied to break these bonds. In the crystalline state this is true and NaCl must be heated to over 800° C before it will melt. When salt is placed in water, however, it can be observed to go into solution quite readily implying that it no longer exist as Na+Cl- crystals, but rather as isolated Na+ and Cl- ions surrounded by water. That this doesn't require 120 kcal/mole becomes clear when the dielectric constant of water replaces that of a vacuum in equation two.
Then V = 120/80 = 1.5 kcal/mole.
It is reasonable to assume that this amount of energy would be available at room temperature. As will be seen later, favorable interactions between water and the ions will also aid dissolution of NaCl in water at room temperature.
Salt does not dissolve in acetone with a dielectric constant of 20 where:
V = 120/20 = 6 kcal/mole
and the interactions between the acetone molecule and the
individual ions are not as favorable. Thus the value of D can
have a great affect on the strength of ionic and other bonds that
depend upon the attraction of charges for their existence.
Secondary Forces
Ion-Dipole Interactions
Covalent bonds may have a partial ionic nature due to unequal electronegativity of the joined atoms. These dipoles may interact with ions or with other dipoles. If a positive ion interacts with a simple linear dipole, the situation exists:
Where d is the distance of separation of the atom and the
dipole and r is the distance the ion is separated from the
dipole. It can be show that:
Define the dipole moment, u, such that:
u = qd 4
which is the charge times its distance of separation. In this case:
u= q2d
Then after rearrangement:
It can be assumed that the distance of separation of the ion from the dipole is much longer than is the covalent bond distance:
d < < r
then: r + d =r
and then:
It is observed that the energy of interaction is proportional
to a constant for the covalent molecule, its dipole moment, and
the charge of the ion. It is inversely proportional to the
dielectric constant and to the distance of separation squared.
Earlier the energy to dissociate NaCl in water was estimated. Now
the favorable energy of association of the Na+ and Cl- ions with
the dipoles of water must be considered. A dielectric constant of
one may be assumed because there can be nothing in between the
molecules of water and the ions. When proper substitutions are
made a value of about - 5 kcal/mole is obtained for each Na+ and
Cl- ion. Thus 10 kcal/mole can be subtracted from the energy
required to dissolve NaCl in water due to the favorable
solute-solvent interactions. Such interactions are undoubtedly
important in the solvation of protein molecules, but are
difficult to quantitate. In general it can be said that each mole
of charge will cause a favorable dipole-ion interaction of about
5 kcal.
Dipole-Dipole Interactions
When two dipoles approach each other they may repel or attract depending on the arrangement of charges. In general, if there is freedom of movement, the forces will align to become attractive. By substituting a dipole for an ion it can be shown that:
In water there should be a large number of attractive interactions due to its dipolar nature. The previous statement concerning the energy requirements of solvation must now be modified. While it is true that there is an energy gain when water molecules interact with charged groups, there is also a loss of energy when the favorable water-water dipole interactions are broken. If the energy gained by the solute-water interactions is greater than the loss due to the breaking of water-water interactions, solution will occur. If the energy gain is less than the loss, the material will be insoluble.
Dipole-dipole interactions can be fairly strong over short
distances, but their force falls with r3 so they
operate over fairly short distances. These forces may be very
important in catalysis where specific alignments of dipoles can
yield substrate-enzyme interactions that are strong and specific.
Only slight changes in the distribution of charges or distance of
separation allows for relatively easy release of the products of
the reaction from the enzyme surface.
Hydrogen Bonds
In proteins, as in water, the most important dipole-dipole interactions involve molecules that contain hydrogen. This leads to a discussion of the hydrogen bond which is a special form of the dipole-dipole interaction. The hydrogen atom consists of only a single proton and an electron. When hydrogen binds covalently to almost any other element, the valence electrons will spend much more time with the other element and a permanent dipole will result. For the compound s-X Hs+ and another compound with a dipole moment s-Y, the molecules will arrange such that:
Hs+ s-Y
And the strength of the dipole-dipole interaction can be calculated. When this is done, however, it is found that the calculated strength is much less than the observed bond strength of from 2 to 6 kcal/mole.
It will also be observed that X and Y will approach much closer to each other than do other dipoles that do not contain hydrogen. This is because hydrogen being a single proton has no electron cloud to repel the electrons of Y and the close approach is allowed. The extra strength of the hydrogen bond is thought to arise from the interaction of some of the electrons of Y and the orbitals of the hydrogen molecule. these special dipole-dipole interactions are very important to proteins for a number of reasons. Many of the properties of water are directly related to its ability to form very strong three dimensional hydrogen bonds. In proteins, the repeating subunit of structure, the peptide bond contains the following groups:
Which tend to form hydrogen bonds whenever possible.
Induced Dipoles
Many groups in protein molecules contain no permanent dipole moment. For instance the:
group of alanine or the:
group of valine. The electron clouds around the molecules are so nearly symmetrical that no dipole moment exist. The charge distribution around such a molecule can be represented as:
If a charged group is placed near the molecule a change in the charge distribution may be induced and thus a dipole moment may be caused to exist such as:
The induced dipole moment mind is expressed as:
where a is a property of a molecule called its polarizability
and can range from 0 to 1. The interaction of the ion with the
individual dipole would then be:
Such interactions are very dependent upon the distance of separation and also upon the dipole moment of the medium. An ion is not the only thing that can induce a dipole. A permanent dipole also has a charge that can induce an attractive electrical interaction in nearby molecules. The strength of the interaction can be shown to be equal to:
and these forces are operative over only very short distances.
London Forces
An electrical neutral molecule might be represented as:
This is only an average conformation and the electrons are actually allowed in a large number of conformations. At any given instant the charge distribution may be more like:
This is called a transient dipole and random motion will cause it to quickly assume a more neutral configuration. If, however, the transient dipole occurs close to a polarizable molecule in a medium of low dielectric constant it can induce a dipole it the neighboring molecule so that the situation as depicted below exist:
The transient dipole induced dipole interaction is always an
attractive one and it tends to stabilize the molecules so that
they behave as weak permanent dipoles as long as their distance
of separation is not too great. These dipoles can now induce
dipoles in neighboring molecules and a large number of weak
attractive forces will be formed. The exact expression for the
bond strength is difficult to evaluate, but it can be shown to be
proportional to r-6. These forces are known as London
dispersion forces and are important in explaining the attraction
of nonpolar molecules for each other.
The Hydrophobic Effect
Proteins contain many nonpolar groups that tend to spontaneously associate away from the aqueous environment. The strength of such attractions are greater than can be explained on the basis of simple London forces and leads to a discussion of the hydrophobic effect.
When the nonpolar portions of a protein or any other molecule are exposed to the aqueous phase, they tend to spontaneously associate in a manner that minimizes contact with water. Measurements of the enthalpy of hydration of a number of nonpolar molecules yield values that are similar and negative. This suggests that there is a favorable interaction between nonpolar molecules and water. When solubility data are are examined, however, it is found that nonpolar molecules are only sparingly soluble in water. Measurements of the free energy of transfer of nonpolar molecules from organic solvents to water give values that are positive. The negative values for the enthalpies of hydration and the positive free energy of transfer to the aqueous phase suggests that the aggregation of nonpolar molecules in an attempt to minimize their contact with water is entropically driven. The intrusion of a nonpolar molecule must interfere with the normal structure of water in such a way as to increase its order.
The ordering of water molecules around nonpolar molecules has been hypothesized to result in the formation of cage-like structures called, chlathrates. This ordering results from an attempt by the water to maintain a maximal number of energetically favorable hydrogen bonds. The decrease in entropy must be balanced by a greater decrease in the enthalpy of the system compared to what would have occurred if the hydrogen bonds had been broken. The net effect is that the energetically most favored state occurs when the area of contact between water and the nonpolar groups is minimized. The association of hydrophobic side chains in the interior of a protein should thus result in an unfavorable increase in enthalpy that is accompanied by an even greater increase in the systems total entropy. In addition the favorable London interactions between hydrophobic groups adds to the stability of the association. This leads to the unusual situation where the associated state is more random than the unassociated state. It also leads to the observation that hydrophobic associations are weakened as the temperature is lowered.
In proteins most of the nonpolar amino acid side chains are located in the interior of the molecules. It has been estimated that the removal of one mole of hydrophobic groups from the surface results in an energy gain of 4 kcal. Thus there is a strong driving force for proteins to bury their hydrophobic groups. Any hydrophobic groups that remain at the surface will increase the total energy of the system. Proteins that have such groups at the surface generally do so for a specific purpose. Many multimeric enzymes, for instance, are held together through the association of hydrophobic groups located at their surfaces
